Not heard from you in a while. Hope you are still with us on this.
I have put together 3 scenarios for inverting your pulse. Each should work but the first 2 have some cons while I favour the 3rd one for simplicity among other things.
Firstly your input pulse (I assume negative going) needs to be as near 5V P-P as you can get it.
My test pulse from a function generator with the datum at zero volts and negative going pulse.
Amplitude 5V P-P, Pule width 200nS. Pulse rise and fall time 15nS. Pulse repetition frequency 500Hz (about half way between your quoted 10Hz and 1kHz).
Pic below as seen on my oscilloscope.
Next is an Op Amp circuit. Unity gain inverting.
The main Con here is the requirement of a split supply which means you would have to find -5V from somewhere, can be done but a bit inconvenient if this is the only place you will use it.
Single supply solution.
First the addition of a 1µF capacitor in series. The resultant Pic here
Here the cap has removed the DC component and actually produced an AC signal. The yellow trace is the input to capacitor and the blue is output. If you look carefully you will note the upper bit has gone to 117mV positive WRT 0V (Ground)This is expected as the Cap has moved Ground to the AVERAGE voltage of the input.
Now this is not much use as it stands so we connect a 10kΩ resistor from this Cap output to VCC. This “biases” this average voltage to VCC value (5V). This shown in the next pic.
Now we have something useful. The blue trace has jumped to a bit over 5V and the pulse going close to ground.
We can now put this through an inverting amplifier as before but without the negative 5V supply.
Now there is a major disadvantage with the use of OpAmps here and that is frequency response and importantly pulse rise and fall time. Unfortunately most of the devices commonly available are Audio types and there is one CA3130 ($6.95) but has the disadvantage at working best an above 8.5V. A bit inconvenient, although quoted at 15MHz the pulse rise time is still pretty poor rise time 0.09µS and settling time of 1.2µS.
There is however an alternative i would use. An inverting Schmidt Trigger. very simple to use, pulse in and inverted pulse out. No extra components. Everything is done for you on chip. You will get almost 5V to almost ground with a rise and fall time of about 20nS. These devices are designed to clean up slow rise and fall signals and generally clean up.Circuit below.
One down side here they are commonly in Hex packages so you will have 5 left over. Ground (or connect to VCC) all unused INPUTS. Do nothing with unused outputs.
I say commonly available as I am looking at a Jaycar catalog as somewhere this sort of thing is available over the counter. They have 74SL14 and 74HC14 which are slightly different but either should do. There may be single or dual units around but I don’t know of any off hand.
I have not tried this as I don’t have a Schmidt Trigger on hand and my nearest Jaycar is 30kM away so I have not been there for a while.
If your pulse is too narrow you may have to stretch it. This will probably need a 555 which is not hard to do with the cap (1µF to about 10nF} value change, the addition of another 10kΩ resistor and a timing resistor and capacitor and a diode or 2 I think… I think the 555 would be fast enough but there might be some faster models around these days. I have not had reason to look